Heron's Formula
Heron's Formula (sometimes called Hero's formula) is a formula for finding the area of a triangle given only the three side lengths.
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[hide]Theorem
For any triangle with side lengths , the area can be found using the following formula:
where the semi-perimeter .
Proof
Proof 2
Imagine a triangle with an altitude dropped from vertex A. Now the side of "a" is split into two sections. Label the right section "x" and the left section "a-x". Now we can prove Heron's formula.
See Also
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In general, it is a good advice not to use Heron's formula in computer programs whenever we can avoid it. For example, whenever vertex coordinates are known, vector product is a much better alternative. Main reasons:
- Computing the square root is much slower than multiplication.
- For triangles with area close to zero Heron's formula computed using floating point variables suffers from precision problems.